Tracking a plane (e.g. floor) with a single camera is a problem solved by a projective transformation. A projective transformation maps lines to lines (but does not necessarily preserve parallelism). Any plane projective transformation can be expressed by an invertible 3×3 matrix in homogeneous coordinates; conversely, any invertible 3×3 matrix defines a projective transformation of the plane. Projective transformations (if not affine) are not defined on all of the plane, but only on the complement of a line (the missing line is “mapped to infinity”). A projective transformation has eight degrees of freedom (8 DOF), and is not a linear transformation and thus, difficult to deal with.
A transformation that preserves lines and parallelism (maps parallel lines to parallel lines) is an affine transformation. An affine transformation has six degrees of freedom.